In known apparatus of the above kind, the conveyance of counterweights from respective storage magazines to the insertion heads, by means of which the counterweights are placed on a wheel to be balanced, is effected by separate feed and conveying lines. Compressed air hoses leading from the individual magazine containers, for different counterweight sizes, to the insertion heads, are used as routes of conveyance for the counterweights. An oscillating conveyor comprising an aligning rail, in which the retaining springs are conveyed to the spring holding means in the insertion heads individually, is used for conveying the retaining springs. Since a corresponding number of magazines is provided for the various sizes of counterweights, and since separate compressed air hoses, through which the counterweights are conveyed to the insertion heads from the magazines are used, a large number of individual conveyance lines is required for the counterweights. Moreover, the retaining springs are conveyed into the insertion heads by conveyance lines provided separately from the counterweight conveyance lines. In this way, coordination of weights and pertinent springs may be achieved by an appropriate control system, but a well defined positioning during the transfer, particularly of the counterweights, is not possible. For this reason, jamming and rise drifts may occur during movement of the counterweights.